mlsanityData to 7 Oct 2026

Dissipative Gradient Descent Ascent Method: A Control Theory Inspired Algorithm for Min-max Optimization

arXiv 2403.09090 ↗First posted 14 Mar 2024math.OC cs.LGcited by 4

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Abstract (arXiv)

Gradient Descent Ascent (GDA) methods for min-max optimization problems typically produce oscillatory behavior that can lead to instability, e.g., in bilinear settings. To address this problem, we introduce a dissipation term into the GDA updates to dampen these oscillations. The proposed Dissipative GDA (DGDA) method can be seen as performing standard GDA on a state-augmented and regularized saddle function that does not strictly introduce additional convexity/concavity. We theoretically show the linear convergence of DGDA in the bilinear and strongly convex-strongly concave settings and assess its performance by comparing DGDA with other methods such as GDA, Extra-Gradient (EG), and Optimistic GDA. Our findings demonstrate that DGDA surpasses these methods, achieving superior convergence rates. We support our claims with two numerical examples that showcase DGDA's effectiveness in solving saddle point problems.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 27 of its 51 references that are in the map. First posted on arXiv 14 Mar 2024.

Builds on

27 of 51 references.

References · 27

  1. 2017Training GANs with Optimismcited by 217
  2. 2018A Variational Inequality Perspective on Generative Adversarial Networkscited by 144
  3. 2019A Unified Analysis of Extra-gradient and Optimistic Gradient Methods for Saddle Point Problems: Proximal Point Approachcited by 142
  4. 2020Near-Optimal Algorithms for Minimax Optimizationcited by 119
  5. 2014Analysis and Design of Optimization Algorithms via Integral Quadratic Constraintscited by 105
  6. 2018Interaction Matters: A Note on Non-asymptotic Local Convergence of Generative Adversarial Networkscited by 68
  7. 2020A Single-Loop Smoothed Gradient Descent-Ascent Algorithm for Nonconvex-Concave Min-Max Problemscited by 57
  8. 2018Banach Wasserstein GANcited by 56
  9. 2020A Unified Single-loop Alternating Gradient Projection Algorithm for Nonconvex-Concave and Convex-Nonconcave Minimax Problemscited by 56
  10. 2016Connecting Generative Adversarial Networks and Actor-Critic Methodscited by 49
  11. 2021Faster Single-loop Algorithms for Minimax Optimization without Strong Concavitycited by 47
  12. 2021Stochastic Gradient Descent-Ascent and Consensus Optimization for Smooth Games: Convergence Analysis under Expected Co-coercivitycited by 43
15 more
  1. 2020Accelerated Zeroth-Order and First-Order Momentum Methods from Mini to Minimax Optimizationcited by 39
  2. 2022Stochastic Gradient Descent-Ascent: Unified Theory and New Efficient Methodscited by 37
  3. 2021Stochastic Extragradient: General Analysis and Improved Ratescited by 31
  4. 2023Last-Iterate Convergent Policy Gradient Primal-Dual Methods for Constrained MDPscited by 27
  5. 2017Dissipativity Theory for Nesterov's Accelerated Methodcited by 22
  6. 2017Analysis of Optimization Algorithms via Integral Quadratic Constraints: Nonstrongly Convex Problemscited by 19
  7. 2018A Proximal Alternating Direction Method of Multiplier for Linearly Constrained Nonconvex Minimizationcited by 14
  8. 2019Convergence of Gradient Methods on Bilinear Zero-Sum Gamescited by 12
  9. 2022Universal Gradient Descent Ascent Method for Nonconvex-Nonconcave Minimax Optimizationcited by 11
  10. 2022Smooth Monotone Stochastic Variational Inequalities and Saddle Point Problems: A Surveycited by 10
  11. 2020A Unified Analysis of First-Order Methods for Smooth Games via Integral Quadratic Constraintscited by 9
  12. 2023Discretized Distributed Optimization over Dynamic Digraphscited by 4
  13. 2022Constrained Reinforcement Learning via Dissipative Saddle Flow Dynamicscited by 3
  14. 2017An integral quadratic constraint framework for real-time steady-state optimization of linear time-invariant systemscited by 2
  15. 2020Saddle Flow Dynamics: Observable Certificates and Separable Regularizationcited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 2; 2026: 2.

4 papers.

  1. 2025Multiplayer Federated Learning: Reaching Equilibrium with Less Communicationcited by 5
  2. 2025Extragradient Method for (L0, L1)-Lipschitz Root-finding Problemscited by 3
  3. 2026Energy-Based Dynamical Models for Neurocomputation, Learning, and Optimizationcited by 1
  4. 2026On Same-Sample and Independent-Sample Stochastic Extragradient for Monotone Variational Inequalitiescited by 0